The decomposition of the Hilbert space into irreducible representations of \(G\)  and the structure constants of the operator product algebra define CFT data. The CFT data completely determines the theory, in the sense that it allows for the computation of all correlation functions. In the conformal bootstrap, one tries to constrain the CFT data from self-consistency and some basic physical requirements. The most constraining consistency conditions are the ones implied by the associativity of the operator product algebra. Usually, this condition is formulated as a property of four-point correlation functions called the crossing symmetry. Therefore, from the mathematical perspective, the bootstrap is a classification programme for solutions of crossing symmetry equations. It was formulated in the 70s by three groups [1]}, [2]}, [3]}, but little progress in dimensions higher than two was made until 2008 when it was realised in [4]} that crossing equations can be efficiently studied numerically. Since then, there have been many significant advances, both in numerical and in analytical studies of bootstrap equations, exemplified by the precise determination of critical exponents in three-dimensional Ising model, [5]}, [6]}, [7]}. Still, no exact solutions beyond the free theory are known in dimensions higher than two.
